| Indicator ID | NA |
| Indicator Name | Pollinator Indicators |
| Country | Norway |
| Continent | Europe |
| Ecosystem Condition Typology Class | NA |
| Realm | Terrestrial (T) |
| Biome | NA |
| Ecosystem | NA |
| Year added | 2024 |
| Last update | 2024 |
| status | incomplete |
| Version | 000.001 |
| Version comment | First draft |
| url | https://github.com/NINAnor/ecRxiv |
Pollinator Indicators
Pollinator potential indicators
1. Introduction
We aim to model the diversity of pollinators in Norway given their know interaction with some plant species. From the estimated diversity across the nation, we intend to look at the estimates in the ASO Data meadows by using their values as the reference values. To achieve this, we do the following:
- obtain data from the Global Biodiversity Infrastructure Facility (GBIF ) for bumblebees, butterflies and bees.
- fit an integrated species distribution model (ISDM) to the data to obtain the distribution of pollinators
- obtain a web plot interaction matrix of the pollinator and plant species
- get data on the plant species within the interaction matrix from GBIF
- fit an ISDM data obtained in step (d) to estimate their respective species occurrence probability
- estimate the alpha diversity index of the pollinators across Norway using the results obtained in (b), (c) and (d).
2. About the underlying data
The pollinator (GBIF.Org User 2024a) and plant species (GBIF.Org User 2024b) data used to fit the ISDMs were obtained from GBIF. The data was downloaded via the R-package rgbif (Chamberlain et al. 2024), and extract the associated metadata using the same R-package. We downloaded GBIF data contains \(26\) datasets and \(30\) datasets with records on pollinators and plants respectively. We present a summary of the datasets downloaded for the pollinator and plant species respectively in Table 5 and Table 6 respectively.
From the metadata, we ascertain the type of each dataset: either presence-only, presence-absence or count data. We merge all the presence-only data into one dataset (which we call mergedDatasetPO), but we do not merge the rest of the datasets. This is because the presence-absence data (procesed from sampling event protocols) have different sampling protocols, and we would like to preserve their unique attributes. A summary of the formatted dataset used to fit the ISDMs are presented in Table 2 and Table 3.
| Dataset name | No. of bees occurrences | No. of butterflies occurrences | No. of hoverflies occurrences |
|---|---|---|---|
| mergedDatasetPO | 22316 | 61009 | 17555 |
| National insect monitoring in Norway | 182 | 157 | 241 |
| Saproxylic insects caught in window traps and hatched from polypores in small and large old forests in southern Norway | 5 | 5 | 5 |
| Solitary bees collected in a large-scale field experiment in power line clearings, southeast Norway | 391 | 0 | 0 |
| Freshwater benthic invertebrates ecological collection NTNU University Museum | 3560 | 3569 | 5433 |
| Bumble bees collected in a large-scale field experiment in power line clearings, southeast Norway | 78 | 0 | 0 |
| Bumblebees and butterflies in Norway | 5687 | 5192 | 0 |
| Freshwater pelagic invertebrates ecological collection NTNU University Museum | 1573 | 1573 | 1574 |
| Species | mergedDatasetPO | Monitoring data of natural and man-made semi-natural meadows in and around Oslo, Norway 2018-2021 | Vegetation data with and without experimental warming, alpine Finse 2000, 2004, 2011 | Effects of vegetation clearing on vascular plants in power line clearings southeast Norway | Vascular plants in power line clearings and the nearby forest, southeast Norway | Overvåking av semi-naturlig eng (ASO) |
|---|---|---|---|---|---|---|
| Ajuga pyramidalis | 4003 | 22 | 720 | 1533 | 599 | 153 |
| Astragalus alpinus | 1851 | 22 | 720 | 1533 | 599 | 153 |
| Campanula rotundifolia | 11703 | 22 | 720 | 1533 | 599 | 153 |
| Carum carvi | 2584 | 22 | 720 | 1533 | 599 | 153 |
| Filipendula ulmaria | 15967 | 22 | 720 | 1533 | 599 | 153 |
| Galium album | 3624 | 22 | 720 | 1533 | 599 | 153 |
| Galium aparine | 1722 | 22 | 720 | 1533 | 599 | 153 |
| Galium boreale | 7360 | 22 | 720 | 1533 | 599 | 153 |
| Galium elongatum | 1399 | 22 | 720 | 1533 | 599 | 153 |
| Galium palustre | 2180 | 22 | 720 | 1533 | 599 | 153 |
| Galium saxatile | 1299 | 22 | 720 | 1533 | 599 | 153 |
| Galium uliginosum | 1761 | 22 | 720 | 1533 | 599 | 153 |
| Galium verum | 3276 | 22 | 720 | 1533 | 599 | 153 |
| Geranium robertianum | 5497 | 22 | 720 | 1533 | 599 | 153 |
| Geranium sylvaticum | 13861 | 22 | 720 | 1533 | 599 | 153 |
| Gymnadenia conopsea | 3179 | 22 | 720 | 1533 | 599 | 153 |
| Hieracium murorum | 20 | 22 | 720 | 1533 | 599 | 153 |
| Hieracium umbellatum | 3663 | 22 | 720 | 1533 | 599 | 153 |
| Hieracium vulgatum | 26 | 22 | 720 | 1533 | 599 | 153 |
| Hypochaeris radicata | 1287 | 22 | 720 | 1533 | 599 | 153 |
| Knautia arvensis | 6030 | 22 | 720 | 1533 | 599 | 153 |
| Lathyrus linifolius | 6118 | 22 | 720 | 1533 | 599 | 153 |
| Lathyrus pratensis | 5458 | 22 | 720 | 1533 | 599 | 153 |
| Lathyrus vernus | 2013 | 22 | 720 | 1533 | 599 | 153 |
| Leucanthemum vulgare | 9160 | 22 | 720 | 1533 | 599 | 153 |
| Lotus corniculatus | 11190 | 22 | 720 | 1533 | 599 | 153 |
| Nardus stricta | 5966 | 22 | 720 | 1533 | 599 | 153 |
| Origanum vulgare | 2178 | 22 | 720 | 1533 | 599 | 153 |
| Plantago lanceolata | 5091 | 22 | 720 | 1533 | 599 | 153 |
| Plantago major | 6525 | 22 | 720 | 1533 | 599 | 153 |
| Plantago media | 2045 | 22 | 720 | 1533 | 599 | 153 |
| Silene dioica | 6888 | 22 | 720 | 1533 | 599 | 153 |
| Silene vulgaris | 3343 | 22 | 720 | 1533 | 599 | 153 |
| Stellaria graminea | 7784 | 22 | 720 | 1533 | 599 | 153 |
| Stellaria media | 3723 | 22 | 720 | 1533 | 599 | 153 |
| Stellaria nemorum | 3694 | 22 | 720 | 1533 | 599 | 153 |
| Trifolium medium | 4394 | 22 | 720 | 1533 | 599 | 153 |
| Trifolium pratense | 11519 | 22 | 720 | 1533 | 599 | 153 |
| Trifolium repens | 10479 | 22 | 720 | 1533 | 599 | 153 |
| Trollius europaeus | 2856 | 22 | 720 | 1533 | 599 | 153 |
| Valeriana sambucifolia | 106 | 22 | 720 | 1533 | 599 | 153 |
| Veronica alpina | 403 | 22 | 720 | 1533 | 599 | 153 |
| Veronica chamaedrys | 8302 | 22 | 720 | 1533 | 599 | 153 |
| Veronica officinalis | 10738 | 22 | 720 | 1533 | 599 | 153 |
| Veronica serpyllifolia | 711 | 22 | 720 | 1533 | 599 | 153 |
| Vicia cracca | 9257 | 22 | 720 | 1533 | 599 | 153 |
| Vicia sepium | 5705 | 22 | 720 | 1533 | 599 | 153 |
| Vicia sylvatica | 1969 | 22 | 720 | 1533 | 599 | 153 |
| Viola biflora | 2990 | 22 | 720 | 1533 | 599 | 153 |
| Viola canina | 3163 | 22 | 720 | 1533 | 599 | 153 |
| Viola epipsila | 423 | 22 | 720 | 1533 | 599 | 153 |
| Viola palustris | 7853 | 22 | 720 | 1533 | 599 | 153 |
| Viola riviniana | 8650 | 22 | 720 | 1533 | 599 | 153 |
| Viola tricolor | 3667 | 22 | 720 | 1533 | 599 | 153 |
2.1 Spatial and temporal resolution
Both pollinator and plant data obtained on a National scale (entire Norway) observed within \(2010\) to \(2024\). We present an illustration of the spatial distribution of the pollinator in the merged Presence-only and National insect monitoring in Norway datasets across the study region in Figure 2.
Iintend to keep either the table or the figures in the final document, depending on what is needed for the report.
2.2 Original units
The original unit of the each dataset obtained from GBIF for the pollinators and plants are provided in Table 5 and Table 6 respectively. The dataset are either presence-only and presence-absence.
2.3 Additional comments about the dataset
3. Indicator properties
Anders will help with this
3.1. ECT
3.2. Ecosystem condition characteristic
3.3. Other standards
3.4. Collinearities with other indicators
4. Reference condition and values
4. 1. Reference condition
4. 2. Reference values
4.2.1 Minimum and maximum values
Reference values for diversity indices at the ASO data meadows.
4.2.2. Threshold value for defining good ecological condition (if relevant)
4.2.3. Spatial resolution and validity
5. Uncertainties
6. References
7. Datasets
Here, we describe each of the dataset used for the modelling. We refer the readers to the dataset description provided on the GBIF website.
| Dataset | Link to description |
|---|---|
| Bumble bees collected in a large-scale field experiment in power line clearings, southeast Norway | https://www.gbif.org/dataset/19fe96b0-0cf3-4a2e-90a5-7c1c19ac94ee |
| Bumblebees and butterflies in Norway | https://www.gbif.org/dataset/19fe96b0-0cf3-4a2e-90a5-7c1c19ac94ee |
| Ecofact | https://www.gbif.org/dataset/19fe96b0-0cf3-4a2e-90a5-7c1c19ac94ee |
| Entomological collections, UiB | [link](https://www.gbif.org/dataset/19fe96b0-0cf3-4a2e-90a5-7c1c19ac94ee) |
| Entomology collection, UiT Tromsø Museum | NA |
| Entomology, Oslo (O) UiO | NA |
| Freshwater benthic invertebrates ecological collection NTNU University Museum | NA |
| Freshwater pelagic invertebrates ecological collection NTNU University Museum | NA |
| Insect collection, UiT, University Museum (TSZ). Insect labeling project and PhD-duty-work | NA |
| Insects of the Forest-Tundra Ecotone (ForTunE) | NA |
| Invertebrate collections, UiB | NA |
| Jordal | NA |
| Lepidoptera collection, South Norway | NA |
| Mapping and monitoring of the Glanville fritillary Melitaea cinxia | NA |
| NINA insect database | NA |
| NORSC - Sciaroidea, UiT Tromsø Museum | NA |
| National insect monitoring in Norway | https://www.gbif.org/dataset/19fe96b0-0cf3-4a2e-90a5-7c1c19ac94ee |
| Norwegian Biodiversity Information Centre - Other datasets | NA |
| Norwegian Species Observation Service | NA |
| Observation.org, Nature data from around the World | NA |
| Occurrence data from various smaller projects in Norway | NA |
| Saproxylic insects caught in window traps and hatched from polypores in small and large old forests in southern Norway | https://www.gbif.org/dataset/19fe96b0-0cf3-4a2e-90a5-7c1c19ac94ee |
| Solitary bees collected in a large-scale field experiment in power line clearings, southeast Norway | NA |
| Terrestrial and limnic invertebrates systematic collection, NTNU University Museum | NA |
| iNaturalist Research-grade Observations | NA |
| naturgucker | NA |
Here, intend to link all the datasets to their correct version on the GBIF repository.
7.1 Pollinator datasets
| Dataset name | Data type | No. of observations | Percent |
|---|---|---|---|
| Bumble bees collected in a large-scale field experiment in power line clearings, southeast Norway | SAMPLING_EVENT | 5016 | 0.28 |
| Bumblebees and butterflies in Norway | SAMPLING_EVENT | 31112 | 1.75 |
| Ecofact | OCCURRENCE | 2 | 0.00 |
| Entomological collections, UiB | OCCURRENCE | 2757 | 0.16 |
| Entomology collection, UiT Tromsø Museum | OCCURRENCE | 2 | 0.00 |
| Entomology, Oslo (O) UiO | OCCURRENCE | 63124 | 3.56 |
| Freshwater benthic invertebrates ecological collection NTNU University Museum | SAMPLING_EVENT | 11559 | 0.65 |
| Freshwater pelagic invertebrates ecological collection NTNU University Museum | SAMPLING_EVENT | 17 | 0.00 |
| Insect collection, UiT, University Museum (TSZ). Insect labeling project and PhD-duty-work | OCCURRENCE | 2048 | 0.12 |
| Insects of the Forest-Tundra Ecotone (ForTunE) | OCCURRENCE | 216 | 0.01 |
| Invertebrate collections, UiB | OCCURRENCE | 14 | 0.00 |
| Jordal | OCCURRENCE | 48 | 0.00 |
| Lepidoptera collection, South Norway | OCCURRENCE | 613 | 0.03 |
| Mapping and monitoring of the Glanville fritillary Melitaea cinxia | OCCURRENCE | 785 | 0.04 |
| NINA insect database | OCCURRENCE | 21342 | 1.20 |
| NORSC - Sciaroidea, UiT Tromsø Museum | OCCURRENCE | 6886 | 0.39 |
| National insect monitoring in Norway | insectMonitoring | 610146 | 34.41 |
| Norwegian Biodiversity Information Centre - Other datasets | OCCURRENCE | 21 | 0.00 |
| Norwegian Species Observation Service | OCCURRENCE | 971031 | 54.75 |
| Observation.org, Nature data from around the World | OCCURRENCE | 4636 | 0.26 |
| Occurrence data from various smaller projects in Norway | OCCURRENCE | 7 | 0.00 |
| Saproxylic insects caught in window traps and hatched from polypores in small and large old forests in southern Norway | SAMPLING_EVENT | 122 | 0.01 |
| Solitary bees collected in a large-scale field experiment in power line clearings, southeast Norway | SAMPLING_EVENT | 2699 | 0.15 |
| Terrestrial and limnic invertebrates systematic collection, NTNU University Museum | OCCURRENCE | 32654 | 1.84 |
| iNaturalist Research-grade Observations | OCCURRENCE | 6456 | 0.36 |
| naturgucker | OCCURRENCE | 99 | 0.01 |
Out of the 26 datasets obtained from GBIF, over half of the total occurrence reports for the pollinators were from the Norwegian species Observation Service, a third of the total occurrence report were from the National insect monitoring in Norway, and the other 24 datasets cover 22 percent of the total pollinator occurrences.
After processing the data, it is important that we filter only the bees from the following datasets: Solitary bees collected in a large-scale field experiment in power line clearings (southeast Norway), Bumble bees collected in a large-scale field experiment in power line clearings (southeast Norway), as can be seen in Figure 3 and Figure 4.
We also filter out bees and butterflies datasets from the Bumblebees and butterflies in Norway dataset, displayed in Figure 5.
7.2. Plant datasets
From our query for datasets from GBIF, we got a total of 30 datasets which we used to fit the ISDM for the plants. Out of these occurrence records, about 86 percent of these records were from the Norwegian species Observation Service.
| Dataset name | Data type | No. of observations | Percent |
|---|---|---|---|
| ARKO strandeng | OCCURRENCE | 274 | 0.09 |
| Ecofact | OCCURRENCE | 51 | 0.02 |
| Effects of vegetation clearing on vascular plants in power line clearings southeast Norway | SAMPLING_EVENT | 779 | 0.24 |
| Jordal | OCCURRENCE | 5434 | 1.70 |
| Monitoring data of natural and man-made semi-natural meadows in and around Oslo, Norway 2018-2021 | SAMPLING_EVENT | 2310 | 0.72 |
| Norwegian Species Observation Service | OCCURRENCE | 288837 | 90.51 |
| Observation.org, Nature data from around the World | OCCURRENCE | 2993 | 0.94 |
| Occurrence data from various smaller projects in Norway | OCCURRENCE | 775 | 0.24 |
| Overvåking av semi-naturlig eng (ASO) | SAMPLING_EVENT | 1606 | 0.50 |
| Overvåking av åpen grunnlendt kalkmark i Oslofjordområdet | OCCURRENCE | 1781 | 0.56 |
| Pl@ntNet automatically identified occurrences | OCCURRENCE | 3265 | 1.02 |
| Pl@ntNet observations | OCCURRENCE | 443 | 0.14 |
| Stabbetorp - Floristiske registreringer 2016 | OCCURRENCE | 1209 | 0.38 |
| Vascular Plant Herbarium, Oslo (O) UiO | OCCURRENCE | 1006 | 0.32 |
| Vascular Plant Herbarium, UiB | OCCURRENCE | 45 | 0.01 |
| Vascular Plants, Observations, Oslo (O) | OCCURRENCE | 192 | 0.06 |
| Vascular plant herbarium (KMN) UiA | OCCURRENCE | 299 | 0.09 |
| Vascular plant herbarium TRH, NTNU University Museum | OCCURRENCE | 659 | 0.21 |
| Vascular plant herbarium, The Arctic University Museum of Norway (TROM) | OCCURRENCE | 208 | 0.07 |
| Vascular plants in power line clearings and the nearby forest, southeast Norway | SAMPLING_EVENT | 269 | 0.08 |
| Vegetation data with and without experimental warming, alpine Finse 2000, 2004, 2011 | SAMPLING_EVENT | 148 | 0.05 |
| iNaturalist Research-grade Observations | OCCURRENCE | 6509 | 2.04 |
| naturgucker | OCCURRENCE | 28 | 0.01 |
7.3. Covariates
We used several covariates to fit both the pollinator and plant ISDMs. The names of the covariates, their description and source are presented in Table 7. Additionally, we include the indication of whether the covariate is a habitat, trait or climatic variables as well as which of the ISDMs it was used to fit in Table 7. The rasters of the covariates are on \(1\) km resolution.
| Name | Description | Source | Habitat/ Trait/ Climatic | Disribution |
|---|---|---|---|---|
| bio1 | Annual temperature | geodata R-package | Climatic | Pollinator, Plant |
| cellID | 1 km grid cell created from the bio1 raster | NA | Trait | NA |
| Latitude | Latitudinal gradient extracted from the bio1 raster | NA | Trait | Pollinator |
| mBio1 | Mean pollinator annual temperature per each pollinator species | NA | Trait | Pollinator |
| sdBio1 | Standard deviation of pollinator annual temperature per each pollinator species | NA | Trait | Pollinator |
| mLat | Mean pollinator latitude per each pollinator species | NA | Trait | Pollinator |
| sdLat | Standard deviation of pollinator latitude per each pollinator species | NA | Trait | Pollinator |
| RegCom | NA | NA | Trait | Pollinator |
| landCover | Land cover raster | NA | Habitat | Pollinator, Plant |
| soilPh | NA | NA | Habitat | Plant |
| soilCoarseFraction | NA | NA | Habitat | Plant |
| soilOrganicCarbon | NA | NA | Habitat | Plant |
| soilMoisture | NA | NA | Climatic | Plant |
| bio1sq | Square of the annual temperature | NA | Climatic | Pollinator |
| bmInt | Interraction between the annual temperature and mean pollinator annual temperature per each pollinator species | NA | Climatic | Pollinator |
| bmIntsq | square of interraction between the annual temperature and mean pollinator annual temperature per each pollinator species | NA | Climatic | Polinator |
We present the distribution of the covariates described in Table 7 here in Figure 8.
8. Spatial units
9. Analyses
We fitted an ISDM using the point process framework [REF] to the merged pollinator presence-only (PO) and presence-absence (PA) datasets. ISDMs are various observation models that are linked together by a shared ecological process.
9.1. General overview of ISDMs
In this subsection, we present an overview of the ISDMs for general understanding of this document. For further details on ISDM, refer to Isaac et al. (2020), Dorazio (2014) and Fithian et al. (2015). The models are described using the point process framework as described in Adjei et al. (2023). Additionally, we present the description of these models under the assumption that we are fitting a multi-species ISDM.
We model the presence-only data as a Poisson point process model (Illian et al. 2008) with mean intensity \(\lambda_i(s)\) for each species \(i = 1, \ldots, S\), where \(S\) is the number of species.This mean intensity modelled as: \[\begin{equation} \label{eq:int} \ln(\lambda_i(s)) = \beta_{0i} + \beta_{ji} X_j(s) + \omega_i(s) + \eta(s), \end{equation}\] where \(\beta_{0i}\) is the species-specific intercept, \(\beta_{ji}\) is the species-specific effect of covariate \(j\), \(X_j(s)\) is the \(j^{th}\) covariate field, \(\omega_i(s)\) is the species-specific spatial autocorrelation field and \(\eta(s)\) is the bias field. \(\omega_i(s)\) and \(\eta(s)\) are modeled as zero mean Gaussian random field (i.e. \(\omega_i(s) \sim N(0, \Sigma)\), where \(\Sigma\) is a Mat’ern covariance matrix with variance \(\sigma_{i}^2\) and range \(\kappa_i\) and \(\eta(s) \sim N(0, \Sigma_\eta)\), where \(\Sigma_\eta\) is a Mat’ern covariance matrix with variance \(\tau^2\) and range \(\kappa_\eta\)).
We model the presence-absence data with a logistic regression model. Let \(y_i(s)\) be a binary value at location \(s\) with \(0\) indicating absence of species \(i\) and \(1\) indicating presence of species \(i\). Then \(y_i(s) \sim \text{Bernoulli}(\Psi_i(s))\) with: \[ cloglog(\Psi_i(s)) = \beta_{0i} + \beta_{ji} X_j(s) + \omega_i(s) \] where the parameters \(\beta_0\), \(\beta_1\) and \(\omega\) are defined in equation \(\ref{eq:int}\).
All the ISDMs were fitted using the R-package PointedSDMs (Mostert and O’Hara 2023).
9.2. ISDM for pollinators
Using the model framework defined above, we fitted the ISDM to the pollinator dataset obtained from GBIF. Due to memory available, we fit the ISDM seperately for each pollinator.
Code
# Load data and covariates
source("pipeline/dataImport/importPollinatorFromGBIF.R")
source("pipeline/dataImport/environmentalDataImport.R")
# Set the model
model <- PointedSDMs::startSpecies(PointsBeesAndButterfliesAndHoverflies, # list of pollinator dataset (containing both mergedDatasetPA and mergedDatasetPO)
Boundary = regionGeometry, # boundary of the study
Projection = newCrs, # projection
Mesh = meshForProject, #mesh used for the model
speciesEnvironment = TRUE, # Should we have pollinator specific covariate effect
speciesIntercept = TRUE, # TRUE treats the intercept as a random effect, instead of constrained as with a fixed effect
pointsIntercept = FALSE, #should we include intercept for each dataset
pointCovariates = FALSE, #do we have covariates for the presence-only data
responsePA = 'individualCount', # column name of the response values for presence-absence data
# trialsPA = 'trials',
spatialCovariates = envCovsForModel, # raster of spatia covariates
speciesName = 'Taxon', # Names of the species in the datasets
pointsSpatial = NULL, # Do not include a dataset spatial field
speciesSpatial = "replicate") # unique spatial field per species, but they share the same hyperparameters.
# Add second bias field for PO data
model$addBias(datasetNames = 'mergedDatasetPO')9.2.1 Priors
We assume the following priors for the pollinator ISDM:
The probability that the standard deviation of the pollinator spatial field is greater than \(1\) is \(0.1\) (i.e. \(P(\sigma_\omega > 0.1) = 0.1\)).
The probability that the standard deviation of the bias field is greater than \(1\) is \(0.1\) (i.e. \(P(\sigma_\eta > 0.1) = 0.1\))
The probability that the spatial range of the pollinator spatial field is less than \(15\)km is \(0.1\) (i.e \(P(\kappa_\omega < 15) = 0.1\))
The probability that the spatial range of the pollinator spatial field is less than \(15\)km is \(0.1\) (i.e. \(P(\kappa_\eta < 15) = 0.1\))
effects of continuous covariates (all covariates except land cover) and the intercept for each pollinator is assumed to be from a Normal distribution with mean \(0\) and variance of \(1\).
Code
# hyper parameters of the spatial field (shared across species)
model$specifySpatial(Species = TRUE, # define same prior for the all species
prior.sigma = c(1, 0.1), # SD of field variation;
prior.range = c(15, 0.1)) # range of spatial correlation;
model$specifySpatial(Bias = TRUE, # Change the prior
prior.sigma = c(1, 0.1),
prior.range = c(15, 0.1))
model$specifyRandom(
# precision parameter on how much each species' spatial field (how much they can deviate from the shared ___)
speciesGroup = list(model = "iid",
hyper = list(prec = list(prior = "pc.prec",
param = c(0.1, 0.1)))),
# precision parameter on the baseline species occurrence rate
speciesIntercepts = list(prior = 'pc.prec',
param = c(0.1, 0.1)))
# Specify priors for covariate effects (continuous)
covariatesToAddEffects <- c("bio1", "bio.sq", "bmInt", "RegCom", "mBio1", "sdBio1", "sdmInt", "Latitude", "mLat", "sdLat", "mlatInt")
for(covs in covariatesToAddEffects){
model$priorsFixed(Effect = covs,
mean.linear = 0,
prec.linear = 1)
}9.2.2 Fit model and make predictions
We fit the model and make predictions of the pollinator intensity within the study region. We fit the model by using the adaptive strategy of the composite design integration strategy in INLA (Rue, Martino, and Chopin 2009).
Code
modelOptions <- list(num.threads = 4,
control.inla = list(int.strategy = 'ccd',
diagonal = 0.001,
cmin = 0,
strategy = "adaptive",
control.vb= list(enable = FALSE)),
verbose = FALSE,
safe = TRUE,
inla.mode = "experimental")
modelRun <- PointedSDMs::fitISDM(data = model,
options = modelOptions)
# predictions for this model
individualDatasetPreds <- predict(modelRun,
data = ppxl,
predictor = TRUE,
n.samples = 100)9.2.3 Pollinator ISDM validation
We perform a five-fold cross validation to assess the trait effect on the pollinator distribution across the study region.
9.3. ISDM for plant species
Modelling all the \(54\) species required memoey allocations we did not have, so we split the species into groups with \(10\) species in each group. We fitted independent ISDMs for each of the groups.
Code
# PointedSDMs takes a longer time to fit for many species
# The trick to to break it into smaller groups
# The split will be done by the number of present speccies in each location
# I will split it nGroups time
sortedSpecies <- table(asoDatasf$acceptedScientificName)%>%
as.data.frame()%>%
dplyr::arrange(desc(Freq))%>%
select(Var1)%>%
c()
# Set the number of groups
nGroups <- 10
#split the species into groups of 10 species in each
plantSpeciesGroup <- split(sortedSpecies$Var1,
seq(1,
ceiling(length(sortedSpecies$Var1)/nGroups)))Similar to the model the pollinator ISDM, we fitted an ISDM to the \(54\) plant species. The ISDM has species-specific intercept, covariate effect and spatial field (but all the species share the same hyperparameters). We also added a spatial bias field to the observation model for the presence-only dataset.
Code
speciesModelShared <- PointedSDMs::startSpecies(formatPlantData,
Boundary = regionGeometry,
Projection = newCrs,
Mesh = meshForProject,
responsePA = 'individualCount',
speciesEnvironment = TRUE,
speciesIntercept = TRUE,
spatialCovariates = envCovsForPlantSpeciesModel,
speciesName = 'simpleScientificName',
pointsIntercept = FALSE,
pointsSpatial = NULL, # Do not include a dataset spatial field
speciesSpatial = "replicate")
# Add bias spatial field for the PO dataset
speciesModelShared$addBias(datasetNames = 'mergedPlantsPO')9.3.1 Priors
We assume the following priors for the pollinator ISDM:
The probability that the standard deviation of the pollinator spatial field is greater than \(0.1\) is \(0.1\) (i.e. \(P(\sigma_\omega > 0.1) = 0.1\)).
The probability that the standard deviation of the bias field is greater than \(0.1\) is \(0.1\) (i.e. \(P(\sigma_\eta > 0.1) = 0.1\))
The probability that the spatial range of the pollinator spatial field is greater than \(50\) is \(0.1\) (i.e \(P(\kappa_\omega < 50) = 0.1\))
The probability that the spatial range of the pollinator spatial field is greater than \(50\) is \(0.1\) (i.e. \(P(\kappa_\eta < 50) = 0.1\))
Code
# hyper parameters of the spatial field (shared across species)
speciesModelShared$specifySpatial(Species = TRUE, # define same prior for the all species
prior.sigma = c(1, 0.1),
prior.range = c(5, 0.1))
speciesModelShared$specifySpatial(Bias = TRUE, # Change the prior
prior.sigma = c(0.6, 0.1),
prior.range = c(5, 0.1))
# prior for random effects (mesh nodes of spatial field and species intercepts)
speciesModelShared$specifyRandom(
# precision parameter on how much each species' spatial field (how much they can deviate from the shared ___)
speciesGroup = list(model = "iid",
hyper = list(prec = list(prior = "pc.prec",
param = c(0.1, 0.1)))),
# precision parameter on the baseline species occurrence rate
speciesIntercepts = list(prior = 'pc.prec',
param = c(0.1, 0.1))) 9.3.2 Model fitting and predictions
We fit the model by using the adaptive strategy of the composite design integration strategy in INLA.
Code
# specify the model options for INLA
modelOptions <- list(num.threads = 4,
control.inla = list(int.strategy = 'ccd',
diagonal = 0.001,
cmin = 0,
strategy = "adaptive",
control.vb= list(enable = FALSE)),
verbose = FALSE,
safe = TRUE,
inla.mode = "experimental")
# Species-specific spatial effects model
speciesSharedEst <- PointedSDMs::fitISDM(data = speciesModelShared,
options = modelOptions)
# I proceed with the prediction of occupancy probabilities
# over the entire region
individualDatasetPreds <- predict(speciesSharedEst,
data = ppxl,
predictor = TRUE,
n.samples = 500)9.4 Species Interractions
Code
load("../data/webPlot.RData")
#interractionMatrix <- readr::read_csv(paste0(dataFolder,"/interractionsData/interractionMatrix.csv"))
bipartite::plotweb(WebReady[[1]])9.5. Diversity Indices
To define the diversity of the pollinators, we estimate the pollinator intensity given their interaction with the plants species within the location \(s\). This is estimated as: \[\begin{equation} \begin{split} \text{Intensity for intensity} &\propto \text{Estimated pollinator intensity} \times \text{Interraction weight} \times \text{plant species occurrence probability}\\ \implies \lambda^{\star}_i(s) &= \frac{\lambda_i(s) \times w_{ik} \times \Psi_k(s)}{\sum_k \lambda_i(s) \times w_k \times \Psi_k(s)}, \end{split} \end{equation}\] where \(w_k\) is the weight of the interaction between pollinator \(i\) and plant species \(k\), \(\Psi_k(s)\) is the occurrence probability of plant species \(k\) and \(\lambda_i(s)\) is the intensity of pollinator \(i\).
We estimated the Hill’s diversity indices for the pollinators. The Hill’s diversity indices are defined as: \[ H(s) = r_i(s) \times log(r_i(s)); \] where \(r_i(s) = \frac{\lambda^{\star}_i(s)}{\sum_{i} \lambda^{\star}_i(s)}\).
10. Results
10.1. Distribution of pollinators accross Norway
We present the predictions of log-intensity of the pollinators in Figure 9 and its standard error in Figure 10. The log-intensity for the three pollinators: bees, butterflies and hoverflies are similar with standard error close to \(0\). This result can be seen as a direct consequence of the estimates of climatic and trait variables on the pollinator distribution (Figure 11 and Figure 12).
The effects of traits and climatic variables on the pollinator distribution in Figure 11. There is a negative latitudinal effect on bees and butterflies, but a positive effect on hoverflies. However, there is a positive effect of annual temperature on butterflies and bees, but a negative effect on hoverflies. There is an insignificant trait effects on the hoverflies distribution as their credible interval of these covariates includes \(0\). The contrast of this statement is true for the bees and butterflies distribution.
In contrast to the trait and climatic variables, there seems to be … (Figure 12).